Novel conductive $CO_2$ membranes composed of dual phases, molten carbonates and electronic conducting ceramics, were investigated. As the microstructure control of electronic conducting ceramic supports is extremely important to keep the molten carbonates stable in the membranes by a capillary force applied by the pore structure of the supports, we have scrutinized the microstructure of the electronic conducting supports utilizing microscopic images and gas permeability measurement. From the evaluation of the electrical conductivities of the molten carbonates and the electronic conducting ceramic supports, we found that the ionic conductivity of the molten carbonates could determine $CO_2$ flux through the dual phase membranes if the surface exchange rate were relatively high enough.